We are given 5 observations, namely {-51.2, 42.88, -35.15, 41.04, -13.68} for the surface temperatures on an asteroid. We'll assume that these are independent observations from a N(, ²) distribution with given standard deviation = 49. Suppose that we also have a prior distribution on that's Normal with mean 0 and standard deviation 36. If only 2 values of namely 0 and 1 are possible and have prior probabilities 2/3 and 1/3 respectively, test H₀: = 0 versus H₁: = 1.